algebra equation

question 1: ^ = power of
if 3x^2-2x+7=0 then (x-1/3)^2= ?
answer : -20/9 HOW DID THEY GET THAT? I DONT UNDERSTAND IT.

question 2:
the graph of which of the following equations is a straight line parallel to the graph of y = 2x
answer: 2x-y=4 HOW THEY GET THAT?

question 3:
An apartment building contains 12 units consisting of 1 and 2 bedroom apartments that rent for $360 and $450 per month, respectively. When all the units are rented, the total monthly rental is $4950. What is the number of 2 bedroom houses?

answer: 7 I thought I was doing this problem right with multipling 450
with each choice and then subtracting that from 4950 then
dividing that from 360 and thought the right answer would
be the difference I needed to make 12 units
but that didnt work so I dont know how they got that
answer.

question 4:
Have one square with a 125 written inside it. another little square with a 5 written in it. If the 2 square regions in the figures below have the respective areas indicated in the square yards, how many yards of fencing are needed to enclose the two regions?

answer:24(5 root sign over it) if that makes any sense to you. please help me.

question 1: ^ = power of
if 3x^2-2x+7=0 then (x-1/3)^2= ?
answer : -20/9 HOW DID THEY GET THAT? I DONT UNDERSTAND IT.

question 2:
the graph of which of the following equations is a straight line parallel to the graph of y = 2x
answer: 2x-y=4 HOW THEY GET THAT?

question 3:
An apartment building contains 12 units consisting of 1 and 2 bedroom apartments that rent for $360 and $450 per month, respectively. When all the units are rented, the total monthly rental is $4950. What is the number of 2 bedroom houses?

answer: 7 I thought I was doing this problem right with multipling 450
with each choice and then subtracting that from 4950 then
dividing that from 360 and thought the right answer would
be the difference I needed to make 12 units
but that didnt work so I dont know how they got that
answer.

question 4:
Have one square with a 125 written inside it. another little square with a 5 written in it. If the 2 square regions in the figures below have the respective areas indicated in the square yards, how many yards of fencing are needed to enclose the two regions?

answer:24(5 root sign over it) if that makes any sense to you. please help me.

Completing the Square

question 1: ^ = power of
if 3x^2-2x+7=0 then (x-1/3)^2= ?
answer : -20/9 HOW DID THEY GET THAT? I DONT UNDERSTAND IT.

question 2:
the graph of which of the following equations is a straight line parallel to the graph of y = 2x
answer: 2x-y=4 HOW THEY GET THAT?

Question 1

The trick you need to understand here is called Completing the Square, and it goes like this.

First, a 'math-y' word: coefficient, which means the number that's in front of the or (along with its minus sign if it has one). So in your expression, the coefficient of is , and the coefficient of is .

So, this is how you complete the square (it's a bit complicated!):

Step 1: Take the coefficient of outside a bracket, dividing all the other cofficients to make it correct. Like this:

(Do you see how the and the have been divided by , making and ?)

Step 2: Inside the brackets you just made write another pair of brackets that contain: and half the coefficient of in the previous line. That's:

(Do you see what I've done? The coefficient of in the previous line was , and I've halved it to get .)

Step 3: write a power after this new bracket. So that is simply:

Step 4: Subtract the square of the number you just wrote in the new bracket. That number was , and the square of this number is . So:

Step 5: Put back the final number that you had when you first created the original bracket. That was . So:

Step 6: Simplify the fractions. That's , which makes . So we get:

Putting all this together into your equation, we get:

(You can now divide both sides of the equation by 3, and leave out the outer brackets, if you like. If it's just an expression, not an equation, you can't do this; you have to leave the 3 there.)

Re-arrange the equation:

Question 2

Is much easier. It's all to do with gradients. Three things you need to know:

1 How to re-arrange equations like into something like
2 The gradient of the line whose equation is is , the coefficient of .

3 Parallel lines have equal gradients.

So, in your question, the gradient of is .

Re-arrange :

The gradient of this line is also , so the lines are parallel.

OK?

Grandad

Last edited by Grandad; Oct 16th 2009 at 03:01 AM.
Reason: More informative title

girl in distress, thank you so much for posting this! you have no idea how happy I am that I found this. For anyone who doesn't know, these are questions from the collegeboard ACCUPLACER exam sample questions. I have been trying to find help on these forever.